Mathematics High School

help the question is on the image.

Answers

Answer 1

Answer:

[tex]\boxed {tan\theta = \frac{2}{3}}[/tex]

Step-by-step explanation:

Let's derive a formula :

⇒ Area (triangle) × 3 = Area (square)

⇒ 1/2(bh) × 3 = a²

∴ But a = h (shown in diagram)

⇒ 3/2(bh) = h²

⇒ h = 3b/2

Now, taking tan θ :

⇒ tan θ = b/h

⇒ tan θ = b/(3b/2)

⇒ tan θ = 2b/3b

⇒ tan θ = 2/3

Related Questions

who is father of math?

Answers

Answer:

Archimedes

Step-by-step explanation:

Archimedes is known as the Father Of Mathematics.

Answer:

Archimedes

Archimedes is known as the Father Of Mathematics

Step-by-step explanation:

Evaluate 5x³ + 2 for x = -1.
0 -3
04
06
0-7

Answers

Answer:

-3

Step-by-step explanation:

5x³ + 2 , when x = -1

5(-1)³ + 2

= -5 + 2

= -3

Answer:

-3

(first option listed)

Step-by-step explanation:

we know that 5x³ + 2 is our expression

we want to "evaluate" (find/solve for) when x = -1

we can do this by plugging in -1 to the expression:

5x³ + 2 {note, x = -1}

5(-1)³ + 2 {-1³ = -1}

5(-1) + 2

(-5) + 2

-5 + 2 = - 3

so, when x = -1, the statement is equivalent to -3

hope this helps! :)

7. Holly plays pool on Sundays. She pays $6.50 for admission and $3.50 for
each round she plays. Which expression can be used to determine how
much she pays if she plays x rounds of pool?

Answers

Answer:

3.50x+6.50=y

Step-by-step explanation:

simplify -9(5 - 2) - 111÷3 show all work

Answers

Answer:

-64

Step-by-step explanation:

use PEMDAS order : Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)

-9(5 - 2) - 111÷3 =

-9(3) - 111÷3 =

-27 - 111÷3 =

-27 - 37 =

-64

Suppose as part of a national study of economic competitiveness a marketing research firm randomly sampled 200 adults between the ages of 27 and 35 living in metropolitan seattle and 180 adults between the ages of 27 and 35 living in metropolitan minneapolis. each adult selected in the sample was asked, among other things, whether they had a college degree. from the seattle sample 66 adults answered yes and from the minneapolis sample 63 adults answered yes when asked if they had a college degree. based on the sample data, can we conclude that there is a difference between the population proportions of adults between the ages of 27 and 35 in the two cities with college degrees

Answers

No we cannot conclude that there is a difference between the population proportion of adults between the ages of 27 and 35 in the two cities.

How to solve for the population proportion

For Seattle

66/200 = 0.33

For Minneapolis

63/180

= 0.35

We have to form our hypothesis

H0: p1 = p2

H1: p1 ≠ p2

We solve for the test statistic

z = (p1-p2)/√(p1*(1-p1)/n1+p2x(1-p2)/n2)

The calculation is given as -0.41

The excel output is given in the attachment

=-0.41

At a significance level of 0.1, the level of acceptance is at -1.645 and 1.645. The value of the test stat can be found here.

Since Z=-0.41 is between -2.58 and 2.58, we do not reject H0.

Hence we fail to reject the null hypothesis.

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suppose your household income increased to $2,000.00 and your energy bill came from $180.00 how many percent of your household income is being spent on electricity?

Answers

hi brainly user! ૮₍ ˃ ⤙ ˂ ₎ა

⊱┈────────────────────────┈⊰

[tex]\large \bold {ANSWER}[/tex]

[tex]\implies \boxed{\underline{\huge{\tt{\orange{\: \: 9\% \: \: }}}}}[/tex]

9% of the family income is being spent to pay the energy bill.

[tex]\large \bold {SOLUTION}[/tex]

HOW TO FIND OUT THE PERCENTAGE?

If your income is now $2,000.00 and you have withdrawn $180.00 from the value, then we say that the $2,000.00 is equivalent to 100% of the value, that is, the total amount. And the amount that was withdrawn will be X because we still don't know how much percent is equivalent to $ 180.00 of this value.

To solve, we will use the simple rule of three like this:

[tex]\frac{2000}{180} = \frac{100}{x}[/tex]

With this we will multiply the denominator of one with the numerator of the other, being:

2000 * X and 180 * 100Where: 2000 * x is equal to 2000xAnd 180 * 100 is equal to 18,000

Knowing this, we will solve it this way:

2000x = 18,000

To start we will isolate the unknown(x) from the values taking the 2000 to the other side of the equality turning it into the denominator of 18,000.

[tex]x = \frac{18000}{2000}[/tex]

And to finish, we cut the 3 zeros of the numerator with the d 3 zeros of the denominator getting 18 / 2. Now it's just dividing.

[tex]\begin{gathered}x = \frac{18}{2} \\ \\ x = 9\end{gathered}[/tex]

We can conclude that the amount spent to pay the energy bill is equivalent to 9% of the family income.

Find x and y. please help ty!! :)

Answers

answer:

x=74 y=27

steps:

triangle in the middle is

180-126 = 54

180-85 = 95

180-149 = 31

126=2x+1+31

126=2x+32

2x=94

x=74

126+2y=180

2y=54

y=27

Alexa needs 20.5 pints of blueberries to
jam. She picked 7.75 pints on Friday and
pints on Saturday. How many more pints
she need to pick?

Answers

Answer:

Your question does not make much sense but that was only because you were missing one variable which was 4.25 which was what you picked up on Saturday. but anyways you just add 7.75 and 4.25 and you'd end up with 12 so she has 12 pints of the blueberries she needs and to find out the remanding you just subtract from the 20.5 but its better to look at it like 20.50 because that's what it is and then you subtract 12 from 20.50 and you are left with 8.50.

Your answer is 8.5

raios of 3 The ratboys to 5 girls

Answers

5/3 = g/24 where g is the number of girls for 24 boys. Typing 5/3 = g/24 into the math tutoring calculator gives us g = 40.

PLEASE HELP IT IS DUE AT 11:15

Answers

Answer:

35, 31, 25, 18

Step-by-step explanation:

10 x 7/2 = 35

10 + 7 + 14 = 31

8 1/3 x 6/2 = 25

4 1/3 + 5 1/3 + 8 1/3 = 18

Two linear equations are shown.
C
654321₁
4
66
y=1/3x+2
y=4/3x-5
What is the solution to the system of equations?
O (7.4)
0 (7.33)
O
0 (8)
O
O (9.7)

Answers

Answer: Option (2)

Step-by-step explanation:

Setting the equations equal to each other,

[tex]\frac{1}{3}x+2=\frac{4}{3}x-5\\\\7=x[/tex]

If x=7, then [tex]y=\frac{7}{3}+2=\frac{13}{3}[/tex]

Determine the solution to the system of equations graphed below and explain your reasoning and complete sentences
g(x)=-2x-3
f(x)= |x+1|-4

Answers

Answer:

(x, y) = (0, -3)

Step-by-step explanation:

On a graph, the solution to a system of equations is the set of points where the graphs of the equations intersect.

solution

The graphs for this system of equations intersect at the point (0, -3). That point is the only solution for this system of equations.

The solution is (x, y) = (0, -3).

In calm water, the motorboat of Jana is moving at the speed of 16.5km/h. On a river, because of the current, the boat moves faster down the river only by raising it. Jana went up the river in 5 hours and the decent in only 2 hours. What is the speed of the current?

Answers

Answer: 707 km/h

Step-by-step explanation:

let c = speed of current

16.5 + c = speed of sailboat downstream

16.5 - c = speed of sailboat upstream

distance = travel time * speed

﹋﹋﹋﹋﹋﹋﹋﹋﹋﹋﹋﹋﹋﹋﹋﹋﹋﹋﹋

2(16.5 + c) = 5(16.5 - c)

33 + 2c = 82.5 - 5c

7c = 49.5

c = 7.07 km/h

Find the remainder when f(X)=2x^3+2x^2-3x-3 is divided by X-2

Answers

The remainder when f(x) = 2x³ + 2x² - 3x - 3 is divided by x - 2 is 15.

We know that the remainder theorem states that if a polynomial p(x) is divided by a linear polynomial q(x) whose zero is x = a, then the remainder is given by r = p(a).

Here p(x) = f(x) = 2x³ + 2x² - 3x - 3 and q(x) = x - 2. First, we have to find the zero of q(x).

Now, q(x) = 0

i.e. x - 2 = 0

i.e. x = 2.

So, the zero of q(x) is 2, i.e. a = 2.

Then by the remainder theorem,

r = p(a) = f(2) = 2(2)³ + 2(2)² - 3(2) - 3 = 2 × 8 + 2 × 4 - 6 - 3 = 16 + 8 - 9 = 16 - 1 = 15

We can conclude that the remainder when f(x) = 2x³ + 2x² - 3x - 3 is divided by x - 2 is 15.

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There are 5 types of fruit in a basket. There are 3 apples, 2 bananas, 4 oranges, 5 kiwi,
and 1 passionfruit. You ask a friend to bring you a piece of fruit. What is the probability of them bringing you an apple?

Answers

The probability of bringing an apple is 0.20

How to determine the probability?

The distribution of the fruits is given as:

3 apples2 bananas4 oranges5 kiwi,1 passion fruit.

The probability of bringing an apple is:

P(Apple) = Apple/Total

This gives

P(Apple) = 3/(3 + 2 + 4 + 5 + 1)

Evaluate

P(Apple) = 0.20

Hence, the probability of bringing an apple is 0.20

Answers

Answer:[tex]x=-\frac{1}{3}, 4[/tex]

Step-by-step explanation:

Graphs intersect the x-axis where y=0, so we can set f(x)=0.

[tex]3x^2 - 11x-4=0 \\ \\ (3x+1)(x-4)=0 \\ \\ x=-\frac{1}{3}, 4[/tex]

Answer:

negative x intercept is at -1/3

positive x intercept 4

Step-by-step explanation:

b) The height of the control tower. a) The shortest distance between the pilot and the base of the control tower. From a horizontal distance of 10.5km, a pilot observes that the angles of depression of the top and base of a control tower are 36° and 41 degrees respectively. Calculate he following:

Answers

From the calculations, the height of the tower is 26.4 Km

What is the angle of depression?

If we know that the base of the tower is B and he top of the tower is T then to find the shortest distance between the pilot and the base of the control tower;

Sin 41 = 10.5//BP/

/BP/ = 10.5/Sin 41

/BP/ = 15.9 Km

Now, the height of the control tower is obtained from;

First /AB/ = √(15.9)^2 - (10.5)^2

/AB/ = 11.9 Km

Given that;

Tan 36 = 10.5//BT/

/BT/= 10.5/Tan 36

/BT/= 14.5 Km

Hence the height of the tower is 11.9 Km + 14.5 Km = 26.4 Km

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PLEASE HELP ME WITH THIS

Answers

Answer:

Decreases

Step-by-step explanation:

A negative correlation means the y is big when the x is small. As x gets bigger, y gets smaller.

urgent please help with this function!!

Answers

Answer:

g(-2) = 0
g(4) = -4

Step-by-step explanation:

-2 works in the second equation because it is within the restrictions, therefore it is 0.
4 works in the third equation because it is within those restrictions, therefor it is -4.

Fill in the blank. In the triangle below, x= Round your answer to two
decimal places.

Answers

Answer:

The answer is 44.80 degrees

Step-by-step explanation:

First you want to find z

z = 180-(52+90)=38

and then try to determine which formula will try to give you x = Tan

Tan = Opposite/ Adjacent

Tan(38)=35/x

x=35/Tan(38)

x=44.80

Kayla has 18 bottles of bubbles. She wants to give 2 bottles to each of her 6 friends. How many bottles will she have left over? Which expression solves the problem?

Expressions:
(18/2)/6
(18/2)+6
(18*2)-6
(18*2)+6

Answers

Answer: she would have 6 bottles left, (18/2)/6

Step-by-step explanation:

she has 18 bottles, when you divide it by two, she could give two bottles to 9 people. but, she only wants to give it to 6 friends. meaning that she would be left with 3 pairs of bubbles. as in, 6 bottles.

Sahil chooses a number, divides it by 8 , adds 8 to the answer. Then multiples the answer with 8 . He obtains the result as 952 . The number he chooses in the beginning was

TAKE POINTS

Answers

Let that be x

(x/8+8)8=952x/8+8=119x/8=119-8x/8=111x=111(8)x=888

The number he chooses, in the beginning, was 888.

How can we interpret the division?

When 'a' is divided by 'b', then the result we get from the division is the part of 'a' that each one of 'b' items will get. Division can be interpreted as equally dividing the number that is being divided into total x parts, where x is the number of parts the given number is divided.

Given that Sahil chooses a number, then divides it by 8, adds 8 to the answer. Then multiply the answer by 8.

Let the unknown number be represented by x.

Therefore,

(x/8+8)8 = 952

x/8+8 = 119

x/8 = 119-8

x/8 = 111

x = 111(8)

x = 888

Therefore, the unknown number would be; 888.

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Juniors and seniors were surveyed about whether they plan to attend a school dance.

94 out of 130 juniors plan to attend.
12 out of 140 seniors do not plan to attend.

The following table shows the results.
(see attachment for table)

What mistake was made in the table?

A. The total for the number of seniors is incorrect
B. The responses for the juniors are reversed
C. The number of juniors attending is incorrect
D. The responses for the seniors is incorrect

Answers

Mistake D. The response from seniors was reversed.

Answer:

The responses for the seniors are reversed.

Hope this helped!

f(x)=√x - 8. Find f¹(x) and its domain.
A. f¹(x) = x² +8; x≥ −8
-1
OB. f¹(x) = x² +8; x20
O c. f¹(x) = (x + 8)²; x≥ −8
O D. f-¹ (x) = (x+8)²; x≥0

Answers

The inverse function is [tex]f^{-1} = (x + 8)^2[/tex], and the domain is the set of all real numbers equal to or larger than -8. So the correct option is C.

How to find the inverse function?

Remember that two functions are inverses if and only if:

[tex]f( f^{-1}(x)) = x\\f^{-1}(f(x)) = x[/tex]

Here we have:

[tex]f(x) = \sqrt{x} - 8[/tex]

Then we want to have:

[tex]f(f^{-1}(x)) = \sqrt{f^{-1}(x)} - 8 = x[/tex]

Solving that for the inverse function, we get:

[tex]f^{-1} = (x + 8)^2[/tex]

Now, how to get the domain. The domain of the inverse function is equal to the range of the original function.

[tex]f(x) = \sqrt{x} - 8[/tex]

The range of f(x) is the set of all real numbers larger or equal than -8 (because the smallest value that x can take is 0).

Then the domain of the inverse function is the set of all real numbers equal to or larger than -8.

The correct option is C.

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Jack have 34 toy cars, Mike says he have 3 times more than Jack's toy cars. How many toy cars does Mike have?

Answers

Answer:102

Step-by-step explanation:

34 x 3 = 102

Answer:

102

Step-by-step explanation:

Since Jack has 34 toy cars and Mike has 3 times more than Jack's toys, we should multiply 34 with 3 to get the answer.

34 * 3 = 102

So, this means that Mike has 102 toy cars.\

Hope this helps :)

Which graph represents the following system of inequalities?
y<-2x+4
yx<3

Answers

A graph which represents the given system of inequalities is Graph C.

What is an inequality?

An inequality can be defined as a mathematical relation that compares two (2) or more integers and variables in an equation based on any of the following:

Less than (<).Greater than (>).Less than or equal to (≤).Greater than or equal to (≥).

Based on the graph for the given system of inequalities (see attachment), we can infer and logically conclude that Graph C best represents them.

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Factorise completely

qn: 12axy + 8bxy + 4xy

Answers

Answer:

Step-by-step explanation:

Answer:

4xy(3a+2b+1)

Step-by-step explanation:

1) Find the Greatest Common Factor (GCF).

1 - What is the largest number that divides evenly into 12axy, 8bxy and 4xy?

It is 4.

2 - What is the highest degree of [tex]a[/tex] that divides evenly into 12axy, 8bxy and 4xy?

It is 1, since a is not in every term.

3 - What is the highest degree of [tex]x[/tex] that divides evenly into 12axy, 8bxy and 4xy?

It is x.

4 - What is the highest degree of [tex]y[/tex] that divides evenly into 12axy, 8bxy and 4xy?

It is y.

5 - What is the highest degree of [tex]b[/tex] that divides evenly into 12axy, 8bxy and 4xy?

It is 1, since [tex]b[/tex] is not in every term.

6 - Multiplying the results above,

GCF = 4xy

2) Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)

[tex]4xy(\frac{12axy}{4xy} +\frac{8bxy}{4xy} +\frac{4xy}{4xy} )[/tex]

3) Simplify each term in parentheses.

[tex]4xy(3a+2b+1)[/tex]

What is the solution to this rational equation? 24/x-8=4

Answers

Answer:

X = 14

24/x-8 = 4

Multiplying both the sides with x-8

24 = (x-8)*4

24 = 4x - 32

24 + 32 = 4x

56 = 4x

56/4 = X

14= X

2(2x – 1) + 7 < 13 or –2x + 5≤-10

Answers

Answer:

x<2 or x ≥ 15/2

Step-by-step explanation:

look at the attachments

the last one at the bottomm c is200

please i really need help its khan

Answers

Answer:

all I know is the second on about world population in 2014 which was c

7•10⁹

Answer:

Step-by-step explanation:

there are 9 steps for the second question so it 10^9

and if you times the 1st population size by 20 you get very close to the second population size.

Other Questions

help the question is on the image.​

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help the question is on the image.